I don't think that Dostoevsky's underground man is experiencing existential boredom. If he were, I think he might be psychologically advancing! Experiencing existential boredom would mean that he recognizes the futility of his life and the idea that his consciousness in being in the world exists in the Sisyphus paradigm: Rolling the rock up the hill, seeing it roll down, and rolling it up again, and so on. This would be where existential boredom resides. Yet, the underground man is far too intense for this. The fact that he recognizes that a world of increasing and encroaching rationality is around him is something that he actively combats against. This is far from existential boredom. The hurting of his liver as an act of social and political resistance go against the idea of existential boredom. Consider his statement on the constant pain of his liver:
My liver hurts? Good, let it hurt even more!
This one statement would indicate that there is little existential boredom in the underground man. He is actively campaigning against his world, his state of being, the entire surroundings that envelop him. The fact that the narrator expresses disdain for human beings as ones that lack fathers and will someday be "born of ideas" represents a reality that is far from existential boredom.
The final piece that would show a lack of embracing existential boredom would be the underground man's interactions with Liza. There is so much here in terms of emotions experienced that do not correspond with existential boredom. The weaving of a narrative where he rescues her, the poet saving the prostitute, is not one borne out of boredom. What is the source, we, and even he, lacks understanding, but it is not an embrace of existential boredom. The shame he experiences when she sees her and with her nobility in the face of his cowardice are all representations of situations where there is no existential boredom, but the stunning shame of simply being a human being. I don't see this as boredom in the existential sense as much as a despairing agony that this is all the underground man can be, indicating displaced hope and a lack of existential reality.